{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:U7BDFTCMKJ63AESSL43MGEFMBS","short_pith_number":"pith:U7BDFTCM","schema_version":"1.0","canonical_sha256":"a7c232cc4c527db012525f36c310ac0c8330a7902e21e81242d5ab99b0e1ad89","source":{"kind":"arxiv","id":"1209.6275","version":1},"attestation_state":"computed","paper":{"title":"A sharp lower bound for some Neumann eigenvalues of the Hermite operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"B. Brandolini, C. Trombetti, F. Chiacchio","submitted_at":"2012-09-27T16:32:44Z","abstract_excerpt":"This paper deals with the Neumann eigenvalue problem for the Hermite operator defined in a convex, possibly unbounded, planar domain $\\Omega$, having one axis of symmetry passing through the origin. We prove a sharp lower bound for the first eigenvalue $\\mu_1^{odd}(\\Omega)$ with an associated eigenfunction odd with respect to the axis of symmetry. Such an estimate involves the first eigenvalue of the corresponding one-dimensional problem. As an immediate consequence, in the class of domains for which $\\mu_1(\\Omega)=\\mu_1^{odd}(\\Omega)$, we get an explicit lower bound for the difference between"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1209.6275","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-27T16:32:44Z","cross_cats_sorted":[],"title_canon_sha256":"03aa3cad65e8674b07da818b2e95516c3acfee3748fa4f088f20d79bdb4149ee","abstract_canon_sha256":"571b639441e159a6eee0533467f784d5f323764689e54203350c5272a9f0a5a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:34.788661Z","signature_b64":"5G52PQ1jxikj7OOzsJKdwItE1lkifCkWNuvOgNWgPtp0chJMJDcAeuuyRNhbutE2x6A2yh5QpGINLGymjUAeAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7c232cc4c527db012525f36c310ac0c8330a7902e21e81242d5ab99b0e1ad89","last_reissued_at":"2026-05-18T03:44:34.787947Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:34.787947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A sharp lower bound for some Neumann eigenvalues of the Hermite operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"B. Brandolini, C. Trombetti, F. Chiacchio","submitted_at":"2012-09-27T16:32:44Z","abstract_excerpt":"This paper deals with the Neumann eigenvalue problem for the Hermite operator defined in a convex, possibly unbounded, planar domain $\\Omega$, having one axis of symmetry passing through the origin. We prove a sharp lower bound for the first eigenvalue $\\mu_1^{odd}(\\Omega)$ with an associated eigenfunction odd with respect to the axis of symmetry. Such an estimate involves the first eigenvalue of the corresponding one-dimensional problem. As an immediate consequence, in the class of domains for which $\\mu_1(\\Omega)=\\mu_1^{odd}(\\Omega)$, we get an explicit lower bound for the difference between"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6275","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1209.6275","created_at":"2026-05-18T03:44:34.788064+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.6275v1","created_at":"2026-05-18T03:44:34.788064+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.6275","created_at":"2026-05-18T03:44:34.788064+00:00"},{"alias_kind":"pith_short_12","alias_value":"U7BDFTCMKJ63","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"U7BDFTCMKJ63AESS","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"U7BDFTCM","created_at":"2026-05-18T12:27:23.164592+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/U7BDFTCMKJ63AESSL43MGEFMBS","json":"https://pith.science/pith/U7BDFTCMKJ63AESSL43MGEFMBS.json","graph_json":"https://pith.science/api/pith-number/U7BDFTCMKJ63AESSL43MGEFMBS/graph.json","events_json":"https://pith.science/api/pith-number/U7BDFTCMKJ63AESSL43MGEFMBS/events.json","paper":"https://pith.science/paper/U7BDFTCM"},"agent_actions":{"view_html":"https://pith.science/pith/U7BDFTCMKJ63AESSL43MGEFMBS","download_json":"https://pith.science/pith/U7BDFTCMKJ63AESSL43MGEFMBS.json","view_paper":"https://pith.science/paper/U7BDFTCM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.6275&json=true","fetch_graph":"https://pith.science/api/pith-number/U7BDFTCMKJ63AESSL43MGEFMBS/graph.json","fetch_events":"https://pith.science/api/pith-number/U7BDFTCMKJ63AESSL43MGEFMBS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U7BDFTCMKJ63AESSL43MGEFMBS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U7BDFTCMKJ63AESSL43MGEFMBS/action/storage_attestation","attest_author":"https://pith.science/pith/U7BDFTCMKJ63AESSL43MGEFMBS/action/author_attestation","sign_citation":"https://pith.science/pith/U7BDFTCMKJ63AESSL43MGEFMBS/action/citation_signature","submit_replication":"https://pith.science/pith/U7BDFTCMKJ63AESSL43MGEFMBS/action/replication_record"}},"created_at":"2026-05-18T03:44:34.788064+00:00","updated_at":"2026-05-18T03:44:34.788064+00:00"}